Det Ch Insp Phil Jones said it was possible the killer had kept the grey knee-length ski sock as a macabre trophy, and issued an urgent appeal to the public to help find it in the hope that it could be the vital clue that will crack the case.

Mr Jones said he was “keeping an open mind” on the possibility that the size 5 sock had been used as the murder weapon, and on the suggestion that the killer kept it as a souvenir.

Miss Yeates is thought to have been murdered on Dec 17, the night she was last seen alive, after returning home just before 9pm following drinks with friends at a pub.

Mr Jones has stepped up the inquiry by adding another 10 officers to his team, making a total of 80 officers working full-time on the case.

He said he was still anxious to trace the driver of a light-coloured 4x4 vehicle seen in Longwood Lane on the night Miss Yeates disappeared, and his officers were trying to rule out “hundreds” of vehicles captured on CCTV as they drove across the Clifton Suspension Bridge, the most likely route the killer would have taken to get to where Miss Yeates’s body was found.

A Facebook page set up by the police to appeal for fresh witnesses has been viewed nearly 250,000 times since it was set up on Tuesday, with 267 phone calls and 75 emails with potential leads coming into the incident room since Monday afternoon, when Mr Jones made his last appeal.

It means police have now received almost 1,700 tip-offs, of which well over 200 are being treated as priority lines of inquiry.

Mr Jones insisted he was happy with the progress of the inquiry, saying: “I will emphasise once again that this is a complex investigation and we are meticulously investigating.”